**Problem Statement**Let $ G $ be a group and let $ H, K $ be subgroups of $ G $ such that $ |H| = 12 $ and $ |K| = 5 $. Prove that $ H \cap K = \{ e \} $.---**Explanation**This problem involves understanding properties of group theory, specifically focusing on subgroups and their intersections. Given that $ |H| $ and $ |K| $ are their respective orders, the task is to demonstrate that their intersection is trivial, only consisting of the identity element of the group $ G $.

Answered: 4. Let G be a group and let H, K be…

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4. Let G be a group and let H, K be subgroups of G such that |H| = 12 and |K| = 5. Prove that HNK = {e

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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**Problem Statement**

Let $ G $ be a group and let $ H, K $ be subgroups of $ G $ such that $ |H| = 12 $ and $ |K| = 5 $. Prove that $ H \cap K = \{ e \} $.

---

**Explanation**

This problem involves understanding properties of group theory, specifically focusing on subgroups and their intersections. Given that $ |H| $ and $ |K| $ are their respective orders, the task is to demonstrate that their intersection is trivial, only consisting of the identity element of the group $ G $.

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